I'm guessing a bit on this date. In have no definitive info.
My reference source says Thank Your Lucky Stars television
program (but I've learned to not trust all photo references).
However, Ringo's drumhead is blank which would put it in January.

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Lewisohn: "Secured for them by Dick James, this was far and
away The Beatles' most important televison appearance to date,
a taping for the very popular and almost fully networked Thank Your
Lucky Stars. Most of Britains' teenage population saw this weekly pop programme... For most viewers, it was their first sight of the Beatles."

The Beatles performed "Please Please Me".
The program was broadcast 19 January